Searches for Violation of CPT Symmetry and Lorentz Invariance with Astrophysical Neutrinos

Neutrinos are a powerful tool for searching physics beyond the standard model of elementary particles. In this review, we present the status of the research on charge-parity-time (CPT) symmetry and Lorentz invariance violations using neutrinos emitted from the collapse of stars such as supernovae and other astrophysical environments, such as gamma-ray bursts. Particularly, supernova neutrino fluxes may provide precious information because all neutrino and antineutrino flavors are emitted during a burst of tens of seconds. Models of quantum gravity may allow the violation of Lorentz invariance and possibly of CPT symmetry. Violation of Lorentz invariance may cause a modification of the dispersion relation and, therefore, in the neutrino group velocity as well in the neutrino wave packet. These changes can affect the arrival time signal registered in astrophysical neutrino detectors. Direction or time-dependent oscillation probabilities and anisotropy of the neutrino velocity are manifestations of the same kind of new physics. CPT violation, on the other hand, may be responsible for different oscillation patterns for neutrino and antineutrino and unconventional energy dependency of the oscillation phase or of the mixing angles. Future perspectives for possible CPT and Lorentz violating systems are also presented.

A Robust Estimation of Lorentz Invariance Violation and Intrinsic Spectral Lag of Short Gamma-Ray Bursts

Gamma-ray bursts (GRBs) have been identified as one of the most promising sources for Lorentz invariance violation (LIV) studies due to their cosmological distance and energetic emission in wide energy bands. However, the arrival-time difference of GRB photons among different energy bands is affected not only by the LIV effect but also by the poorly known intrinsic spectral lags. In previous studies, assumptions of spectral lag have to be made which could introduce systematic errors. In this paper, we used a sample of 46 short GRBs (SGRBs), whose intrinsic spectra lags are much smaller than long GRBs, to better constrain the LIV. The observed spectral lags are derived between two fixed energy bands in the source rest frame rather than the observer frame. Moreover, the lags are calculated with the novel Li–CCF method, which is more robust than traditional methods. Our results show that, if we consider LIV as a linear energy dependence of the photon propagation speed in the data fit, then we obtain a robust limit of E QG > 1015 GeV (95% CL). If we assume no LIV effect in the keV–MeV energy range, the goodness of data fit is equivalently as well as the case with LIV and we can constrain the common intrinsic spectral lags of SGRBs to be 1.4 ± 0.5 ms (1σ), which is the most accurate measurement thus far.

Lorentz Violation by the Preferred Frame Effects and Cosmic and Gamma Ray Propagation

The ‘relativity with a preferred frame’, designed to reconcile the relativity principle with the existence of the cosmological preferred frame, incorporates the preferred frame at the level of special relativity (SR) while retaining the fundamental spacetime symmetry, which, in the standard SR, manifests itself as Lorentz invariance. In this paper, the processes, accompanying the propagation of cosmic rays and gamma rays through the background radiation from distant sources to Earth, are considered on the basis of particle dynamics and electromagnetic field dynamics developed within the framework of the ‘relativity with a preferred frame’. Applying the theory to the photopion-production and pair-production processes shows that the modified particle dynamics and electrodynamics lead to measurable signatures in the observed cosmic and gamma-ray spectra which can provide an interpretation of some puzzling features found in the observational data. Other processes responsible for gamma-ray attenuation are considered. It is found, in particular, that electromagnetic cascades, developing on cosmic microwave background and extragalactic background light, may be reduced or suppressed due to the preferred frame effects which should influence the shape of the very high-energy gamma-ray spectra. Other possible observational consequences of the theory, such as the birefringence of light propagating in vacuo and dispersion, are discussed.

Proving the Lorentz Invariance of the Entropy and the Covariance of Thermodynamics

The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked in the proof are that there is at least one inertial reference frame in which the second law of thermodynamics is valid and that the microscopic theory describing the internal dynamics of the body is a field theory, with Lorentz invariant Lagrangian density. The proof makes no reference to the connection between entropy and probabilities and is valid both within classical and quantum physics. To avoid any risk of circular reasoning, we do not postulate that the laws of thermodynamics are the same in every reference frame, but we obtain this fact as a direct consequence of the Lorentz invariance of the entropy.

Cosmology and Cosmic Rays Propagation in the Relativity with a Preferred Frame

In this chapter, cosmological models and the processes accompanying the propagation of the cosmic rays on cosmological scales are considered based on particle dynamics, electrodynamics and general relativity (GR) developed from the basic concepts of the ‘relativity with a preferred frame’. The ‘relativity with a preferred frame’, designed to reconcile the relativity principle with the existence of the cosmological preferred frame, incorporates the preferred frame at the fundamental level of special relativity (SR) while retaining the fundamental space-time symmetry which, in the standard SR, manifests itself as Lorentz invariance. The cosmological models based on the modified GR of the ‘relativity with a preferred frame’ allow us to explain the SNIa observational data without introducing the dark energy and also fit other observational data, in particular, the BAO data. Applying the theory to the photo pion-production and pair-production processes, accompanying the propagation of the Ultra-High Energy Cosmic Rays (UHECR) and gamma rays through the universal diffuse background radiation, shows that the modified particle dynamics, electrodynamics and GR lead to measurable signatures in the observed cosmic rays spectra which can provide an interpretation of some puzzling features found in the observational data. Other possible observational consequences of the theory, such as the birefringence of light propagating in vacuo and dispersion, are discussed.

Hadron wave functions in high-energy scattering, form factors and strong decays: The effects of the Lorentz contracted form

In this paper, we study the class of the processes, where dynamics depends essentially on the properties of the hadron wave functions involved in the reactions. In this case, the momentum dependence of the form of the wave functions, imposed by the Lorentz invariance and in particular by the Lorentz contraction, can be tested in the experiment and may strongly influence the resulting cross-sections. One example of such observables is given by the hadron form factors in the case when the large [Formula: see text] behavior is mostly frozen, while the Lorentz contraction of the hadron wave functions is taken into account. Another example, considered earlier, is the strong hadron decay with high-energy emission. In this paper, we study the role of the Lorentz contraction in the high-energy hadron–hadron scattering process at large momentum transfer. For the [Formula: see text] and [Formula: see text] scattering at large [Formula: see text], it is shown that at small [Formula: see text], the picture of two exponential slopes in the differential cross-section, explained previously by the author, remains stable, while the backward scattering cross-section is strongly increased by the Lorentz contraction.

Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

Prospects for the Detection of the Prompt Very-high-energy Emission from γ-ray Bursts with the High Altitude Detection of Astronomical Radiation Experiment

The observation of very-high-energy (VHE; > 10 GeV) γ-ray emission from γ-ray bursts (GRBs), especially in the prompt phase, will provide critical information for understanding many aspects of their nature including the physical environment, the relativistic bulk motion, the mechanisms of particle acceleration of GRBs, and for studying Lorentz invariance violation, etc. For the afterglow phase, the highest-energy photons detected to date by the imaging atmospheric Cherenkov telescopes extend to the TeV regime. However, for the prompt phase, years of efforts in searching for the VHE emission has yielded no statistically significant detections. A wide field of view and large effective area above tens of GeV are essential for detecting the VHE emissions from GRBs in the prompt phase. The High Altitude Detection of Astronomical Radiation (HADAR) experiment has such merits. In this paper, we report the estimates of its expected annual GRB detection rate, which are obtained by combining the performance of the HADAR instrument with the theoretical calculations based on a phenomenological model to generate the pseudo-GRB population. The expected detectable gamma-ray signal from GRBs above the background is then obtained to give the detection rate. In the spectral model, an extra component is assigned to every GRB event in addition to the Band function. The results indicate that if the energy of the cutoff due to internal absorption is higher than 50 GeV, the detection rate for GRBs for the HADAR experiment is approximately two or three GRBs per year, which varies slightly depending upon the characteristics of the extra component.

On the Lorentz-Invariance of the Dyson Series in Theories with Derivative Couplings

We study the Dyson series for the S-matrix, when the interaction depends on derivatives of the fields. We concentrate on two particular examples: the scalar electrodynamics and the renormalized ф4 theory. By using Wick’s theorem, we eventually give evidence that the Lorentz invariance is satisfied, and the usual Feynman rules can be applied to the interaction Lagrangian.

Anisotropic scaling for 3D topological models

A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent $$\nu$$ ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent $$\theta =\nu _{x}/\nu _{z}$$ θ = ν x / ν z . We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for $$\nu$$ ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation $$\nu _{\bar{\alpha }}z_{\bar{\alpha }}=2q$$ ν α ¯ z α ¯ = 2 q and $$\theta =\nu _{x}/\nu _{z}=z_{z}/z_{x}$$ θ = ν x / ν z = z z / z x for $$\nu$$ ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction $$\bar{\alpha }$$ α ¯ . An anisotropic quantum hyperscaling relation is also obtained.